Rolling bearing fault has the characteristics of compound signal and strong environmental noise. By building an over- complete dictionary that is sensitive to the rolling bearing fault, the basis pursuit is used to obtain the optimal sparse representa- tion of compound signal. The excellent effect of time-frequency structure of impulse can be acquired, and the noise can be reduced. The fault characteristic frequency is proved to be specific from the spectral analysis results of reconstructed signals. The analysis results of simulating data and experimental data show that the proposed method ha...